The following generalizations of Euler's formula are known in the art:fm(t)=et·cos(21-mπ)ei·t·sin(21-mπ)  (1)fm(t)=eti(22-m)  (2)
In these equations, i is the imaginary constant equal to √{square root over (−1)}, t is the time parameter, and m has the effect of varying the geometry of the curve. m=2 corresponds to a complex circle, as the above reduce to the Euler term eti. Known telecommunication signaling techniques such as the Quadrature Amplitude Modulation technique (“QAM technique”) are based on complex circles. Values of m>2 correspond to complex spirals of increasingly rapid growth, and increasingly lower frequency.